The Polaris/Pole star and revolution of Earth

Question

How can we say that the Pole star is fixed just because it is positioned exactly above the North Pole? How does it revolve along with Earth around the Sun if it's fixed?

Answer 1

We can't say anything is "fixed" - it is only ever "somewhat fixed relative to x", where x might be our frame of reference. Further, while the radius of the Earth's orbit is about 150 million km, the distance to Polaris is $4\cdot 10^{15}km$. When you move Earth by 300 million km (the approximate diameter of its orbit), the apparent angle to Polaris would change by $7.5\cdot 10^{-7}~\rm{rad}$ which is about 0˚00'00.15" - really a very small shift that you won't normally be able to detect. For comparison, the sextant NASA developed for space flight had an rms error of 8.6 arcsec source - see page 8 - over 50x greater than the shift in apparent position of Polaris.

In fact, Earth's axis doesn't point directly at Polaris (see this article)- and the direction it's pointing changes all the time. This phenomenon is called precession - it is a result of the fact that the earth is not a perfect sphere, but slightly bulging at the equator. As a consequence, gravity of the Sun pulls a little harder on the near side than the far side of the equator, and this differential force creates a torque on the Earth. When a spinning object is subject to torque, it starts precessing (see my link).

In the case of Earth, the rate of precession is about 26,000 years. That means that Polaris is "moving" through the sky at a much higher rate than the 0.15 arcsec/ 6 months that I calculated above.

Answer 2

The answer to both questions is that the star-earth distance is very very far.

First, because of this, there is only little apparent motions of the stars in the course of human civilization history.

Second, due to the same reason, the earth's axis always points to Polaris in the course of one year, no matter where it is in the orbit around the sun.

By the way, Polaris is not "fixed". But it is because of the precession of the Earth's rotation axis. Tens of thousands of years later, Vega will be the "North Star".